# Properties

 Label 3630.2.a.n.1.1 Level $3630$ Weight $2$ Character 3630.1 Self dual yes Analytic conductor $28.986$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 3630.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$28.9856959337$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 330) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## Embedding invariants

 Embedding label 1.1 Character $$\chi$$ $$=$$ 3630.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} -2.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -8.00000 q^{19} -1.00000 q^{20} +4.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -2.00000 q^{29} +1.00000 q^{30} +8.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} -8.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} -6.00000 q^{41} -8.00000 q^{43} -1.00000 q^{45} +4.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} -2.00000 q^{52} +2.00000 q^{53} -1.00000 q^{54} +8.00000 q^{57} -2.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} +6.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -12.0000 q^{67} +2.00000 q^{68} -4.00000 q^{69} -12.0000 q^{71} +1.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} -1.00000 q^{75} -8.00000 q^{76} +2.00000 q^{78} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} -8.00000 q^{86} +2.00000 q^{87} -6.00000 q^{89} -1.00000 q^{90} +4.00000 q^{92} -8.00000 q^{93} -4.00000 q^{94} +8.00000 q^{95} -1.00000 q^{96} -14.0000 q^{97} -7.00000 q^{98} +O(q^{100})$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 0.707107
$$3$$ −1.00000 −0.577350
$$4$$ 1.00000 0.500000
$$5$$ −1.00000 −0.447214
$$6$$ −1.00000 −0.408248
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 1.00000 0.353553
$$9$$ 1.00000 0.333333
$$10$$ −1.00000 −0.316228
$$11$$ 0 0
$$12$$ −1.00000 −0.288675
$$13$$ −2.00000 −0.554700 −0.277350 0.960769i $$-0.589456\pi$$
−0.277350 + 0.960769i $$0.589456\pi$$
$$14$$ 0 0
$$15$$ 1.00000 0.258199
$$16$$ 1.00000 0.250000
$$17$$ 2.00000 0.485071 0.242536 0.970143i $$-0.422021\pi$$
0.242536 + 0.970143i $$0.422021\pi$$
$$18$$ 1.00000 0.235702
$$19$$ −8.00000 −1.83533 −0.917663 0.397360i $$-0.869927\pi$$
−0.917663 + 0.397360i $$0.869927\pi$$
$$20$$ −1.00000 −0.223607
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 4.00000 0.834058 0.417029 0.908893i $$-0.363071\pi$$
0.417029 + 0.908893i $$0.363071\pi$$
$$24$$ −1.00000 −0.204124
$$25$$ 1.00000 0.200000
$$26$$ −2.00000 −0.392232
$$27$$ −1.00000 −0.192450
$$28$$ 0 0
$$29$$ −2.00000 −0.371391 −0.185695 0.982607i $$-0.559454\pi$$
−0.185695 + 0.982607i $$0.559454\pi$$
$$30$$ 1.00000 0.182574
$$31$$ 8.00000 1.43684 0.718421 0.695608i $$-0.244865\pi$$
0.718421 + 0.695608i $$0.244865\pi$$
$$32$$ 1.00000 0.176777
$$33$$ 0 0
$$34$$ 2.00000 0.342997
$$35$$ 0 0
$$36$$ 1.00000 0.166667
$$37$$ −2.00000 −0.328798 −0.164399 0.986394i $$-0.552568\pi$$
−0.164399 + 0.986394i $$0.552568\pi$$
$$38$$ −8.00000 −1.29777
$$39$$ 2.00000 0.320256
$$40$$ −1.00000 −0.158114
$$41$$ −6.00000 −0.937043 −0.468521 0.883452i $$-0.655213\pi$$
−0.468521 + 0.883452i $$0.655213\pi$$
$$42$$ 0 0
$$43$$ −8.00000 −1.21999 −0.609994 0.792406i $$-0.708828\pi$$
−0.609994 + 0.792406i $$0.708828\pi$$
$$44$$ 0 0
$$45$$ −1.00000 −0.149071
$$46$$ 4.00000 0.589768
$$47$$ −4.00000 −0.583460 −0.291730 0.956501i $$-0.594231\pi$$
−0.291730 + 0.956501i $$0.594231\pi$$
$$48$$ −1.00000 −0.144338
$$49$$ −7.00000 −1.00000
$$50$$ 1.00000 0.141421
$$51$$ −2.00000 −0.280056
$$52$$ −2.00000 −0.277350
$$53$$ 2.00000 0.274721 0.137361 0.990521i $$-0.456138\pi$$
0.137361 + 0.990521i $$0.456138\pi$$
$$54$$ −1.00000 −0.136083
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 8.00000 1.05963
$$58$$ −2.00000 −0.262613
$$59$$ 4.00000 0.520756 0.260378 0.965507i $$-0.416153\pi$$
0.260378 + 0.965507i $$0.416153\pi$$
$$60$$ 1.00000 0.129099
$$61$$ 6.00000 0.768221 0.384111 0.923287i $$-0.374508\pi$$
0.384111 + 0.923287i $$0.374508\pi$$
$$62$$ 8.00000 1.01600
$$63$$ 0 0
$$64$$ 1.00000 0.125000
$$65$$ 2.00000 0.248069
$$66$$ 0 0
$$67$$ −12.0000 −1.46603 −0.733017 0.680211i $$-0.761888\pi$$
−0.733017 + 0.680211i $$0.761888\pi$$
$$68$$ 2.00000 0.242536
$$69$$ −4.00000 −0.481543
$$70$$ 0 0
$$71$$ −12.0000 −1.42414 −0.712069 0.702109i $$-0.752242\pi$$
−0.712069 + 0.702109i $$0.752242\pi$$
$$72$$ 1.00000 0.117851
$$73$$ −2.00000 −0.234082 −0.117041 0.993127i $$-0.537341\pi$$
−0.117041 + 0.993127i $$0.537341\pi$$
$$74$$ −2.00000 −0.232495
$$75$$ −1.00000 −0.115470
$$76$$ −8.00000 −0.917663
$$77$$ 0 0
$$78$$ 2.00000 0.226455
$$79$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$80$$ −1.00000 −0.111803
$$81$$ 1.00000 0.111111
$$82$$ −6.00000 −0.662589
$$83$$ −4.00000 −0.439057 −0.219529 0.975606i $$-0.570452\pi$$
−0.219529 + 0.975606i $$0.570452\pi$$
$$84$$ 0 0
$$85$$ −2.00000 −0.216930
$$86$$ −8.00000 −0.862662
$$87$$ 2.00000 0.214423
$$88$$ 0 0
$$89$$ −6.00000 −0.635999 −0.317999 0.948091i $$-0.603011\pi$$
−0.317999 + 0.948091i $$0.603011\pi$$
$$90$$ −1.00000 −0.105409
$$91$$ 0 0
$$92$$ 4.00000 0.417029
$$93$$ −8.00000 −0.829561
$$94$$ −4.00000 −0.412568
$$95$$ 8.00000 0.820783
$$96$$ −1.00000 −0.102062
$$97$$ −14.0000 −1.42148 −0.710742 0.703452i $$-0.751641\pi$$
−0.710742 + 0.703452i $$0.751641\pi$$
$$98$$ −7.00000 −0.707107
$$99$$ 0 0
$$100$$ 1.00000 0.100000
$$101$$ 6.00000 0.597022 0.298511 0.954406i $$-0.403510\pi$$
0.298511 + 0.954406i $$0.403510\pi$$
$$102$$ −2.00000 −0.198030
$$103$$ 16.0000 1.57653 0.788263 0.615338i $$-0.210980\pi$$
0.788263 + 0.615338i $$0.210980\pi$$
$$104$$ −2.00000 −0.196116
$$105$$ 0 0
$$106$$ 2.00000 0.194257
$$107$$ −20.0000 −1.93347 −0.966736 0.255774i $$-0.917670\pi$$
−0.966736 + 0.255774i $$0.917670\pi$$
$$108$$ −1.00000 −0.0962250
$$109$$ 6.00000 0.574696 0.287348 0.957826i $$-0.407226\pi$$
0.287348 + 0.957826i $$0.407226\pi$$
$$110$$ 0 0
$$111$$ 2.00000 0.189832
$$112$$ 0 0
$$113$$ 2.00000 0.188144 0.0940721 0.995565i $$-0.470012\pi$$
0.0940721 + 0.995565i $$0.470012\pi$$
$$114$$ 8.00000 0.749269
$$115$$ −4.00000 −0.373002
$$116$$ −2.00000 −0.185695
$$117$$ −2.00000 −0.184900
$$118$$ 4.00000 0.368230
$$119$$ 0 0
$$120$$ 1.00000 0.0912871
$$121$$ 0 0
$$122$$ 6.00000 0.543214
$$123$$ 6.00000 0.541002
$$124$$ 8.00000 0.718421
$$125$$ −1.00000 −0.0894427
$$126$$ 0 0
$$127$$ 16.0000 1.41977 0.709885 0.704317i $$-0.248747\pi$$
0.709885 + 0.704317i $$0.248747\pi$$
$$128$$ 1.00000 0.0883883
$$129$$ 8.00000 0.704361
$$130$$ 2.00000 0.175412
$$131$$ −12.0000 −1.04844 −0.524222 0.851581i $$-0.675644\pi$$
−0.524222 + 0.851581i $$0.675644\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −12.0000 −1.03664
$$135$$ 1.00000 0.0860663
$$136$$ 2.00000 0.171499
$$137$$ 2.00000 0.170872 0.0854358 0.996344i $$-0.472772\pi$$
0.0854358 + 0.996344i $$0.472772\pi$$
$$138$$ −4.00000 −0.340503
$$139$$ −16.0000 −1.35710 −0.678551 0.734553i $$-0.737392\pi$$
−0.678551 + 0.734553i $$0.737392\pi$$
$$140$$ 0 0
$$141$$ 4.00000 0.336861
$$142$$ −12.0000 −1.00702
$$143$$ 0 0
$$144$$ 1.00000 0.0833333
$$145$$ 2.00000 0.166091
$$146$$ −2.00000 −0.165521
$$147$$ 7.00000 0.577350
$$148$$ −2.00000 −0.164399
$$149$$ −10.0000 −0.819232 −0.409616 0.912258i $$-0.634337\pi$$
−0.409616 + 0.912258i $$0.634337\pi$$
$$150$$ −1.00000 −0.0816497
$$151$$ 8.00000 0.651031 0.325515 0.945537i $$-0.394462\pi$$
0.325515 + 0.945537i $$0.394462\pi$$
$$152$$ −8.00000 −0.648886
$$153$$ 2.00000 0.161690
$$154$$ 0 0
$$155$$ −8.00000 −0.642575
$$156$$ 2.00000 0.160128
$$157$$ −2.00000 −0.159617 −0.0798087 0.996810i $$-0.525431\pi$$
−0.0798087 + 0.996810i $$0.525431\pi$$
$$158$$ 0 0
$$159$$ −2.00000 −0.158610
$$160$$ −1.00000 −0.0790569
$$161$$ 0 0
$$162$$ 1.00000 0.0785674
$$163$$ 20.0000 1.56652 0.783260 0.621694i $$-0.213555\pi$$
0.783260 + 0.621694i $$0.213555\pi$$
$$164$$ −6.00000 −0.468521
$$165$$ 0 0
$$166$$ −4.00000 −0.310460
$$167$$ −16.0000 −1.23812 −0.619059 0.785345i $$-0.712486\pi$$
−0.619059 + 0.785345i $$0.712486\pi$$
$$168$$ 0 0
$$169$$ −9.00000 −0.692308
$$170$$ −2.00000 −0.153393
$$171$$ −8.00000 −0.611775
$$172$$ −8.00000 −0.609994
$$173$$ −18.0000 −1.36851 −0.684257 0.729241i $$-0.739873\pi$$
−0.684257 + 0.729241i $$0.739873\pi$$
$$174$$ 2.00000 0.151620
$$175$$ 0 0
$$176$$ 0 0
$$177$$ −4.00000 −0.300658
$$178$$ −6.00000 −0.449719
$$179$$ −12.0000 −0.896922 −0.448461 0.893802i $$-0.648028\pi$$
−0.448461 + 0.893802i $$0.648028\pi$$
$$180$$ −1.00000 −0.0745356
$$181$$ −2.00000 −0.148659 −0.0743294 0.997234i $$-0.523682\pi$$
−0.0743294 + 0.997234i $$0.523682\pi$$
$$182$$ 0 0
$$183$$ −6.00000 −0.443533
$$184$$ 4.00000 0.294884
$$185$$ 2.00000 0.147043
$$186$$ −8.00000 −0.586588
$$187$$ 0 0
$$188$$ −4.00000 −0.291730
$$189$$ 0 0
$$190$$ 8.00000 0.580381
$$191$$ −12.0000 −0.868290 −0.434145 0.900843i $$-0.642949\pi$$
−0.434145 + 0.900843i $$0.642949\pi$$
$$192$$ −1.00000 −0.0721688
$$193$$ 22.0000 1.58359 0.791797 0.610784i $$-0.209146\pi$$
0.791797 + 0.610784i $$0.209146\pi$$
$$194$$ −14.0000 −1.00514
$$195$$ −2.00000 −0.143223
$$196$$ −7.00000 −0.500000
$$197$$ −10.0000 −0.712470 −0.356235 0.934396i $$-0.615940\pi$$
−0.356235 + 0.934396i $$0.615940\pi$$
$$198$$ 0 0
$$199$$ −24.0000 −1.70131 −0.850657 0.525720i $$-0.823796\pi$$
−0.850657 + 0.525720i $$0.823796\pi$$
$$200$$ 1.00000 0.0707107
$$201$$ 12.0000 0.846415
$$202$$ 6.00000 0.422159
$$203$$ 0 0
$$204$$ −2.00000 −0.140028
$$205$$ 6.00000 0.419058
$$206$$ 16.0000 1.11477
$$207$$ 4.00000 0.278019
$$208$$ −2.00000 −0.138675
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$212$$ 2.00000 0.137361
$$213$$ 12.0000 0.822226
$$214$$ −20.0000 −1.36717
$$215$$ 8.00000 0.545595
$$216$$ −1.00000 −0.0680414
$$217$$ 0 0
$$218$$ 6.00000 0.406371
$$219$$ 2.00000 0.135147
$$220$$ 0 0
$$221$$ −4.00000 −0.269069
$$222$$ 2.00000 0.134231
$$223$$ −16.0000 −1.07144 −0.535720 0.844396i $$-0.679960\pi$$
−0.535720 + 0.844396i $$0.679960\pi$$
$$224$$ 0 0
$$225$$ 1.00000 0.0666667
$$226$$ 2.00000 0.133038
$$227$$ −12.0000 −0.796468 −0.398234 0.917284i $$-0.630377\pi$$
−0.398234 + 0.917284i $$0.630377\pi$$
$$228$$ 8.00000 0.529813
$$229$$ 14.0000 0.925146 0.462573 0.886581i $$-0.346926\pi$$
0.462573 + 0.886581i $$0.346926\pi$$
$$230$$ −4.00000 −0.263752
$$231$$ 0 0
$$232$$ −2.00000 −0.131306
$$233$$ 18.0000 1.17922 0.589610 0.807688i $$-0.299282\pi$$
0.589610 + 0.807688i $$0.299282\pi$$
$$234$$ −2.00000 −0.130744
$$235$$ 4.00000 0.260931
$$236$$ 4.00000 0.260378
$$237$$ 0 0
$$238$$ 0 0
$$239$$ −16.0000 −1.03495 −0.517477 0.855697i $$-0.673129\pi$$
−0.517477 + 0.855697i $$0.673129\pi$$
$$240$$ 1.00000 0.0645497
$$241$$ −18.0000 −1.15948 −0.579741 0.814801i $$-0.696846\pi$$
−0.579741 + 0.814801i $$0.696846\pi$$
$$242$$ 0 0
$$243$$ −1.00000 −0.0641500
$$244$$ 6.00000 0.384111
$$245$$ 7.00000 0.447214
$$246$$ 6.00000 0.382546
$$247$$ 16.0000 1.01806
$$248$$ 8.00000 0.508001
$$249$$ 4.00000 0.253490
$$250$$ −1.00000 −0.0632456
$$251$$ −20.0000 −1.26239 −0.631194 0.775625i $$-0.717435\pi$$
−0.631194 + 0.775625i $$0.717435\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 16.0000 1.00393
$$255$$ 2.00000 0.125245
$$256$$ 1.00000 0.0625000
$$257$$ 26.0000 1.62184 0.810918 0.585160i $$-0.198968\pi$$
0.810918 + 0.585160i $$0.198968\pi$$
$$258$$ 8.00000 0.498058
$$259$$ 0 0
$$260$$ 2.00000 0.124035
$$261$$ −2.00000 −0.123797
$$262$$ −12.0000 −0.741362
$$263$$ 24.0000 1.47990 0.739952 0.672660i $$-0.234848\pi$$
0.739952 + 0.672660i $$0.234848\pi$$
$$264$$ 0 0
$$265$$ −2.00000 −0.122859
$$266$$ 0 0
$$267$$ 6.00000 0.367194
$$268$$ −12.0000 −0.733017
$$269$$ −22.0000 −1.34136 −0.670682 0.741745i $$-0.733998\pi$$
−0.670682 + 0.741745i $$0.733998\pi$$
$$270$$ 1.00000 0.0608581
$$271$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$272$$ 2.00000 0.121268
$$273$$ 0 0
$$274$$ 2.00000 0.120824
$$275$$ 0 0
$$276$$ −4.00000 −0.240772
$$277$$ 14.0000 0.841178 0.420589 0.907251i $$-0.361823\pi$$
0.420589 + 0.907251i $$0.361823\pi$$
$$278$$ −16.0000 −0.959616
$$279$$ 8.00000 0.478947
$$280$$ 0 0
$$281$$ 10.0000 0.596550 0.298275 0.954480i $$-0.403589\pi$$
0.298275 + 0.954480i $$0.403589\pi$$
$$282$$ 4.00000 0.238197
$$283$$ 8.00000 0.475551 0.237775 0.971320i $$-0.423582\pi$$
0.237775 + 0.971320i $$0.423582\pi$$
$$284$$ −12.0000 −0.712069
$$285$$ −8.00000 −0.473879
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000 0.0589256
$$289$$ −13.0000 −0.764706
$$290$$ 2.00000 0.117444
$$291$$ 14.0000 0.820695
$$292$$ −2.00000 −0.117041
$$293$$ 6.00000 0.350524 0.175262 0.984522i $$-0.443923\pi$$
0.175262 + 0.984522i $$0.443923\pi$$
$$294$$ 7.00000 0.408248
$$295$$ −4.00000 −0.232889
$$296$$ −2.00000 −0.116248
$$297$$ 0 0
$$298$$ −10.0000 −0.579284
$$299$$ −8.00000 −0.462652
$$300$$ −1.00000 −0.0577350
$$301$$ 0 0
$$302$$ 8.00000 0.460348
$$303$$ −6.00000 −0.344691
$$304$$ −8.00000 −0.458831
$$305$$ −6.00000 −0.343559
$$306$$ 2.00000 0.114332
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ −16.0000 −0.910208
$$310$$ −8.00000 −0.454369
$$311$$ −20.0000 −1.13410 −0.567048 0.823685i $$-0.691915\pi$$
−0.567048 + 0.823685i $$0.691915\pi$$
$$312$$ 2.00000 0.113228
$$313$$ −6.00000 −0.339140 −0.169570 0.985518i $$-0.554238\pi$$
−0.169570 + 0.985518i $$0.554238\pi$$
$$314$$ −2.00000 −0.112867
$$315$$ 0 0
$$316$$ 0 0
$$317$$ −6.00000 −0.336994 −0.168497 0.985702i $$-0.553891\pi$$
−0.168497 + 0.985702i $$0.553891\pi$$
$$318$$ −2.00000 −0.112154
$$319$$ 0 0
$$320$$ −1.00000 −0.0559017
$$321$$ 20.0000 1.11629
$$322$$ 0 0
$$323$$ −16.0000 −0.890264
$$324$$ 1.00000 0.0555556
$$325$$ −2.00000 −0.110940
$$326$$ 20.0000 1.10770
$$327$$ −6.00000 −0.331801
$$328$$ −6.00000 −0.331295
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −12.0000 −0.659580 −0.329790 0.944054i $$-0.606978\pi$$
−0.329790 + 0.944054i $$0.606978\pi$$
$$332$$ −4.00000 −0.219529
$$333$$ −2.00000 −0.109599
$$334$$ −16.0000 −0.875481
$$335$$ 12.0000 0.655630
$$336$$ 0 0
$$337$$ −10.0000 −0.544735 −0.272367 0.962193i $$-0.587807\pi$$
−0.272367 + 0.962193i $$0.587807\pi$$
$$338$$ −9.00000 −0.489535
$$339$$ −2.00000 −0.108625
$$340$$ −2.00000 −0.108465
$$341$$ 0 0
$$342$$ −8.00000 −0.432590
$$343$$ 0 0
$$344$$ −8.00000 −0.431331
$$345$$ 4.00000 0.215353
$$346$$ −18.0000 −0.967686
$$347$$ 20.0000 1.07366 0.536828 0.843692i $$-0.319622\pi$$
0.536828 + 0.843692i $$0.319622\pi$$
$$348$$ 2.00000 0.107211
$$349$$ 30.0000 1.60586 0.802932 0.596071i $$-0.203272\pi$$
0.802932 + 0.596071i $$0.203272\pi$$
$$350$$ 0 0
$$351$$ 2.00000 0.106752
$$352$$ 0 0
$$353$$ 26.0000 1.38384 0.691920 0.721974i $$-0.256765\pi$$
0.691920 + 0.721974i $$0.256765\pi$$
$$354$$ −4.00000 −0.212598
$$355$$ 12.0000 0.636894
$$356$$ −6.00000 −0.317999
$$357$$ 0 0
$$358$$ −12.0000 −0.634220
$$359$$ 32.0000 1.68890 0.844448 0.535638i $$-0.179929\pi$$
0.844448 + 0.535638i $$0.179929\pi$$
$$360$$ −1.00000 −0.0527046
$$361$$ 45.0000 2.36842
$$362$$ −2.00000 −0.105118
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 2.00000 0.104685
$$366$$ −6.00000 −0.313625
$$367$$ 16.0000 0.835193 0.417597 0.908633i $$-0.362873\pi$$
0.417597 + 0.908633i $$0.362873\pi$$
$$368$$ 4.00000 0.208514
$$369$$ −6.00000 −0.312348
$$370$$ 2.00000 0.103975
$$371$$ 0 0
$$372$$ −8.00000 −0.414781
$$373$$ −2.00000 −0.103556 −0.0517780 0.998659i $$-0.516489\pi$$
−0.0517780 + 0.998659i $$0.516489\pi$$
$$374$$ 0 0
$$375$$ 1.00000 0.0516398
$$376$$ −4.00000 −0.206284
$$377$$ 4.00000 0.206010
$$378$$ 0 0
$$379$$ 36.0000 1.84920 0.924598 0.380945i $$-0.124401\pi$$
0.924598 + 0.380945i $$0.124401\pi$$
$$380$$ 8.00000 0.410391
$$381$$ −16.0000 −0.819705
$$382$$ −12.0000 −0.613973
$$383$$ 12.0000 0.613171 0.306586 0.951843i $$-0.400813\pi$$
0.306586 + 0.951843i $$0.400813\pi$$
$$384$$ −1.00000 −0.0510310
$$385$$ 0 0
$$386$$ 22.0000 1.11977
$$387$$ −8.00000 −0.406663
$$388$$ −14.0000 −0.710742
$$389$$ −22.0000 −1.11544 −0.557722 0.830028i $$-0.688325\pi$$
−0.557722 + 0.830028i $$0.688325\pi$$
$$390$$ −2.00000 −0.101274
$$391$$ 8.00000 0.404577
$$392$$ −7.00000 −0.353553
$$393$$ 12.0000 0.605320
$$394$$ −10.0000 −0.503793
$$395$$ 0 0
$$396$$ 0 0
$$397$$ −2.00000 −0.100377 −0.0501886 0.998740i $$-0.515982\pi$$
−0.0501886 + 0.998740i $$0.515982\pi$$
$$398$$ −24.0000 −1.20301
$$399$$ 0 0
$$400$$ 1.00000 0.0500000
$$401$$ 18.0000 0.898877 0.449439 0.893311i $$-0.351624\pi$$
0.449439 + 0.893311i $$0.351624\pi$$
$$402$$ 12.0000 0.598506
$$403$$ −16.0000 −0.797017
$$404$$ 6.00000 0.298511
$$405$$ −1.00000 −0.0496904
$$406$$ 0 0
$$407$$ 0 0
$$408$$ −2.00000 −0.0990148
$$409$$ −26.0000 −1.28562 −0.642809 0.766027i $$-0.722231\pi$$
−0.642809 + 0.766027i $$0.722231\pi$$
$$410$$ 6.00000 0.296319
$$411$$ −2.00000 −0.0986527
$$412$$ 16.0000 0.788263
$$413$$ 0 0
$$414$$ 4.00000 0.196589
$$415$$ 4.00000 0.196352
$$416$$ −2.00000 −0.0980581
$$417$$ 16.0000 0.783523
$$418$$ 0 0
$$419$$ 4.00000 0.195413 0.0977064 0.995215i $$-0.468849\pi$$
0.0977064 + 0.995215i $$0.468849\pi$$
$$420$$ 0 0
$$421$$ 38.0000 1.85201 0.926003 0.377515i $$-0.123221\pi$$
0.926003 + 0.377515i $$0.123221\pi$$
$$422$$ 0 0
$$423$$ −4.00000 −0.194487
$$424$$ 2.00000 0.0971286
$$425$$ 2.00000 0.0970143
$$426$$ 12.0000 0.581402
$$427$$ 0 0
$$428$$ −20.0000 −0.966736
$$429$$ 0 0
$$430$$ 8.00000 0.385794
$$431$$ 24.0000 1.15604 0.578020 0.816023i $$-0.303826\pi$$
0.578020 + 0.816023i $$0.303826\pi$$
$$432$$ −1.00000 −0.0481125
$$433$$ 2.00000 0.0961139 0.0480569 0.998845i $$-0.484697\pi$$
0.0480569 + 0.998845i $$0.484697\pi$$
$$434$$ 0 0
$$435$$ −2.00000 −0.0958927
$$436$$ 6.00000 0.287348
$$437$$ −32.0000 −1.53077
$$438$$ 2.00000 0.0955637
$$439$$ 16.0000 0.763638 0.381819 0.924237i $$-0.375298\pi$$
0.381819 + 0.924237i $$0.375298\pi$$
$$440$$ 0 0
$$441$$ −7.00000 −0.333333
$$442$$ −4.00000 −0.190261
$$443$$ −28.0000 −1.33032 −0.665160 0.746701i $$-0.731637\pi$$
−0.665160 + 0.746701i $$0.731637\pi$$
$$444$$ 2.00000 0.0949158
$$445$$ 6.00000 0.284427
$$446$$ −16.0000 −0.757622
$$447$$ 10.0000 0.472984
$$448$$ 0 0
$$449$$ 10.0000 0.471929 0.235965 0.971762i $$-0.424175\pi$$
0.235965 + 0.971762i $$0.424175\pi$$
$$450$$ 1.00000 0.0471405
$$451$$ 0 0
$$452$$ 2.00000 0.0940721
$$453$$ −8.00000 −0.375873
$$454$$ −12.0000 −0.563188
$$455$$ 0 0
$$456$$ 8.00000 0.374634
$$457$$ 38.0000 1.77757 0.888783 0.458329i $$-0.151552\pi$$
0.888783 + 0.458329i $$0.151552\pi$$
$$458$$ 14.0000 0.654177
$$459$$ −2.00000 −0.0933520
$$460$$ −4.00000 −0.186501
$$461$$ −18.0000 −0.838344 −0.419172 0.907907i $$-0.637680\pi$$
−0.419172 + 0.907907i $$0.637680\pi$$
$$462$$ 0 0
$$463$$ 8.00000 0.371792 0.185896 0.982569i $$-0.440481\pi$$
0.185896 + 0.982569i $$0.440481\pi$$
$$464$$ −2.00000 −0.0928477
$$465$$ 8.00000 0.370991
$$466$$ 18.0000 0.833834
$$467$$ 36.0000 1.66588 0.832941 0.553362i $$-0.186655\pi$$
0.832941 + 0.553362i $$0.186655\pi$$
$$468$$ −2.00000 −0.0924500
$$469$$ 0 0
$$470$$ 4.00000 0.184506
$$471$$ 2.00000 0.0921551
$$472$$ 4.00000 0.184115
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −8.00000 −0.367065
$$476$$ 0 0
$$477$$ 2.00000 0.0915737
$$478$$ −16.0000 −0.731823
$$479$$ −24.0000 −1.09659 −0.548294 0.836286i $$-0.684723\pi$$
−0.548294 + 0.836286i $$0.684723\pi$$
$$480$$ 1.00000 0.0456435
$$481$$ 4.00000 0.182384
$$482$$ −18.0000 −0.819878
$$483$$ 0 0
$$484$$ 0 0
$$485$$ 14.0000 0.635707
$$486$$ −1.00000 −0.0453609
$$487$$ 8.00000 0.362515 0.181257 0.983436i $$-0.441983\pi$$
0.181257 + 0.983436i $$0.441983\pi$$
$$488$$ 6.00000 0.271607
$$489$$ −20.0000 −0.904431
$$490$$ 7.00000 0.316228
$$491$$ 12.0000 0.541552 0.270776 0.962642i $$-0.412720\pi$$
0.270776 + 0.962642i $$0.412720\pi$$
$$492$$ 6.00000 0.270501
$$493$$ −4.00000 −0.180151
$$494$$ 16.0000 0.719874
$$495$$ 0 0
$$496$$ 8.00000 0.359211
$$497$$ 0 0
$$498$$ 4.00000 0.179244
$$499$$ 4.00000 0.179065 0.0895323 0.995984i $$-0.471463\pi$$
0.0895323 + 0.995984i $$0.471463\pi$$
$$500$$ −1.00000 −0.0447214
$$501$$ 16.0000 0.714827
$$502$$ −20.0000 −0.892644
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ −6.00000 −0.266996
$$506$$ 0 0
$$507$$ 9.00000 0.399704
$$508$$ 16.0000 0.709885
$$509$$ −22.0000 −0.975133 −0.487566 0.873086i $$-0.662115\pi$$
−0.487566 + 0.873086i $$0.662115\pi$$
$$510$$ 2.00000 0.0885615
$$511$$ 0 0
$$512$$ 1.00000 0.0441942
$$513$$ 8.00000 0.353209
$$514$$ 26.0000 1.14681
$$515$$ −16.0000 −0.705044
$$516$$ 8.00000 0.352180
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 18.0000 0.790112
$$520$$ 2.00000 0.0877058
$$521$$ −38.0000 −1.66481 −0.832405 0.554168i $$-0.813037\pi$$
−0.832405 + 0.554168i $$0.813037\pi$$
$$522$$ −2.00000 −0.0875376
$$523$$ −24.0000 −1.04945 −0.524723 0.851273i $$-0.675831\pi$$
−0.524723 + 0.851273i $$0.675831\pi$$
$$524$$ −12.0000 −0.524222
$$525$$ 0 0
$$526$$ 24.0000 1.04645
$$527$$ 16.0000 0.696971
$$528$$ 0 0
$$529$$ −7.00000 −0.304348
$$530$$ −2.00000 −0.0868744
$$531$$ 4.00000 0.173585
$$532$$ 0 0
$$533$$ 12.0000 0.519778
$$534$$ 6.00000 0.259645
$$535$$ 20.0000 0.864675
$$536$$ −12.0000 −0.518321
$$537$$ 12.0000 0.517838
$$538$$ −22.0000 −0.948487
$$539$$ 0 0
$$540$$ 1.00000 0.0430331
$$541$$ −26.0000 −1.11783 −0.558914 0.829226i $$-0.688782\pi$$
−0.558914 + 0.829226i $$0.688782\pi$$
$$542$$ 0 0
$$543$$ 2.00000 0.0858282
$$544$$ 2.00000 0.0857493
$$545$$ −6.00000 −0.257012
$$546$$ 0 0
$$547$$ −8.00000 −0.342055 −0.171028 0.985266i $$-0.554709\pi$$
−0.171028 + 0.985266i $$0.554709\pi$$
$$548$$ 2.00000 0.0854358
$$549$$ 6.00000 0.256074
$$550$$ 0 0
$$551$$ 16.0000 0.681623
$$552$$ −4.00000 −0.170251
$$553$$ 0 0
$$554$$ 14.0000 0.594803
$$555$$ −2.00000 −0.0848953
$$556$$ −16.0000 −0.678551
$$557$$ 46.0000 1.94908 0.974541 0.224208i $$-0.0719796\pi$$
0.974541 + 0.224208i $$0.0719796\pi$$
$$558$$ 8.00000 0.338667
$$559$$ 16.0000 0.676728
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 10.0000 0.421825
$$563$$ −4.00000 −0.168580 −0.0842900 0.996441i $$-0.526862\pi$$
−0.0842900 + 0.996441i $$0.526862\pi$$
$$564$$ 4.00000 0.168430
$$565$$ −2.00000 −0.0841406
$$566$$ 8.00000 0.336265
$$567$$ 0 0
$$568$$ −12.0000 −0.503509
$$569$$ −14.0000 −0.586911 −0.293455 0.955973i $$-0.594805\pi$$
−0.293455 + 0.955973i $$0.594805\pi$$
$$570$$ −8.00000 −0.335083
$$571$$ 40.0000 1.67395 0.836974 0.547243i $$-0.184323\pi$$
0.836974 + 0.547243i $$0.184323\pi$$
$$572$$ 0 0
$$573$$ 12.0000 0.501307
$$574$$ 0 0
$$575$$ 4.00000 0.166812
$$576$$ 1.00000 0.0416667
$$577$$ 18.0000 0.749350 0.374675 0.927156i $$-0.377754\pi$$
0.374675 + 0.927156i $$0.377754\pi$$
$$578$$ −13.0000 −0.540729
$$579$$ −22.0000 −0.914289
$$580$$ 2.00000 0.0830455
$$581$$ 0 0
$$582$$ 14.0000 0.580319
$$583$$ 0 0
$$584$$ −2.00000 −0.0827606
$$585$$ 2.00000 0.0826898
$$586$$ 6.00000 0.247858
$$587$$ −12.0000 −0.495293 −0.247647 0.968850i $$-0.579657\pi$$
−0.247647 + 0.968850i $$0.579657\pi$$
$$588$$ 7.00000 0.288675
$$589$$ −64.0000 −2.63707
$$590$$ −4.00000 −0.164677
$$591$$ 10.0000 0.411345
$$592$$ −2.00000 −0.0821995
$$593$$ 26.0000 1.06769 0.533846 0.845582i $$-0.320746\pi$$
0.533846 + 0.845582i $$0.320746\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −10.0000 −0.409616
$$597$$ 24.0000 0.982255
$$598$$ −8.00000 −0.327144
$$599$$ −36.0000 −1.47092 −0.735460 0.677568i $$-0.763034\pi$$
−0.735460 + 0.677568i $$0.763034\pi$$
$$600$$ −1.00000 −0.0408248
$$601$$ 22.0000 0.897399 0.448699 0.893683i $$-0.351887\pi$$
0.448699 + 0.893683i $$0.351887\pi$$
$$602$$ 0 0
$$603$$ −12.0000 −0.488678
$$604$$ 8.00000 0.325515
$$605$$ 0 0
$$606$$ −6.00000 −0.243733
$$607$$ −16.0000 −0.649420 −0.324710 0.945814i $$-0.605267\pi$$
−0.324710 + 0.945814i $$0.605267\pi$$
$$608$$ −8.00000 −0.324443
$$609$$ 0 0
$$610$$ −6.00000 −0.242933
$$611$$ 8.00000 0.323645
$$612$$ 2.00000 0.0808452
$$613$$ 38.0000 1.53481 0.767403 0.641165i $$-0.221549\pi$$
0.767403 + 0.641165i $$0.221549\pi$$
$$614$$ 0 0
$$615$$ −6.00000 −0.241943
$$616$$ 0 0
$$617$$ 42.0000 1.69086 0.845428 0.534089i $$-0.179345\pi$$
0.845428 + 0.534089i $$0.179345\pi$$
$$618$$ −16.0000 −0.643614
$$619$$ −20.0000 −0.803868 −0.401934 0.915669i $$-0.631662\pi$$
−0.401934 + 0.915669i $$0.631662\pi$$
$$620$$ −8.00000 −0.321288
$$621$$ −4.00000 −0.160514
$$622$$ −20.0000 −0.801927
$$623$$ 0 0
$$624$$ 2.00000 0.0800641
$$625$$ 1.00000 0.0400000
$$626$$ −6.00000 −0.239808
$$627$$ 0 0
$$628$$ −2.00000 −0.0798087
$$629$$ −4.00000 −0.159490
$$630$$ 0 0
$$631$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −6.00000 −0.238290
$$635$$ −16.0000 −0.634941
$$636$$ −2.00000 −0.0793052
$$637$$ 14.0000 0.554700
$$638$$ 0 0
$$639$$ −12.0000 −0.474713
$$640$$ −1.00000 −0.0395285
$$641$$ 42.0000 1.65890 0.829450 0.558581i $$-0.188654\pi$$
0.829450 + 0.558581i $$0.188654\pi$$
$$642$$ 20.0000 0.789337
$$643$$ −20.0000 −0.788723 −0.394362 0.918955i $$-0.629034\pi$$
−0.394362 + 0.918955i $$0.629034\pi$$
$$644$$ 0 0
$$645$$ −8.00000 −0.315000
$$646$$ −16.0000 −0.629512
$$647$$ −44.0000 −1.72982 −0.864909 0.501928i $$-0.832624\pi$$
−0.864909 + 0.501928i $$0.832624\pi$$
$$648$$ 1.00000 0.0392837
$$649$$ 0 0
$$650$$ −2.00000 −0.0784465
$$651$$ 0 0
$$652$$ 20.0000 0.783260
$$653$$ −30.0000 −1.17399 −0.586995 0.809590i $$-0.699689\pi$$
−0.586995 + 0.809590i $$0.699689\pi$$
$$654$$ −6.00000 −0.234619
$$655$$ 12.0000 0.468879
$$656$$ −6.00000 −0.234261
$$657$$ −2.00000 −0.0780274
$$658$$ 0 0
$$659$$ −4.00000 −0.155818 −0.0779089 0.996960i $$-0.524824\pi$$
−0.0779089 + 0.996960i $$0.524824\pi$$
$$660$$ 0 0
$$661$$ 14.0000 0.544537 0.272268 0.962221i $$-0.412226\pi$$
0.272268 + 0.962221i $$0.412226\pi$$
$$662$$ −12.0000 −0.466393
$$663$$ 4.00000 0.155347
$$664$$ −4.00000 −0.155230
$$665$$ 0 0
$$666$$ −2.00000 −0.0774984
$$667$$ −8.00000 −0.309761
$$668$$ −16.0000 −0.619059
$$669$$ 16.0000 0.618596
$$670$$ 12.0000 0.463600
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 6.00000 0.231283 0.115642 0.993291i $$-0.463108\pi$$
0.115642 + 0.993291i $$0.463108\pi$$
$$674$$ −10.0000 −0.385186
$$675$$ −1.00000 −0.0384900
$$676$$ −9.00000 −0.346154
$$677$$ 38.0000 1.46046 0.730229 0.683202i $$-0.239413\pi$$
0.730229 + 0.683202i $$0.239413\pi$$
$$678$$ −2.00000 −0.0768095
$$679$$ 0 0
$$680$$ −2.00000 −0.0766965
$$681$$ 12.0000 0.459841
$$682$$ 0 0
$$683$$ −4.00000 −0.153056 −0.0765279 0.997067i $$-0.524383\pi$$
−0.0765279 + 0.997067i $$0.524383\pi$$
$$684$$ −8.00000 −0.305888
$$685$$ −2.00000 −0.0764161
$$686$$ 0 0
$$687$$ −14.0000 −0.534133
$$688$$ −8.00000 −0.304997
$$689$$ −4.00000 −0.152388
$$690$$ 4.00000 0.152277
$$691$$ 20.0000 0.760836 0.380418 0.924815i $$-0.375780\pi$$
0.380418 + 0.924815i $$0.375780\pi$$
$$692$$ −18.0000 −0.684257
$$693$$ 0 0
$$694$$ 20.0000 0.759190
$$695$$ 16.0000 0.606915
$$696$$ 2.00000 0.0758098
$$697$$ −12.0000 −0.454532
$$698$$ 30.0000 1.13552
$$699$$ −18.0000 −0.680823
$$700$$ 0 0
$$701$$ 46.0000 1.73740 0.868698 0.495342i $$-0.164957\pi$$
0.868698 + 0.495342i $$0.164957\pi$$
$$702$$ 2.00000 0.0754851
$$703$$ 16.0000 0.603451
$$704$$ 0 0
$$705$$ −4.00000 −0.150649
$$706$$ 26.0000 0.978523
$$707$$ 0 0
$$708$$ −4.00000 −0.150329
$$709$$ 46.0000 1.72757 0.863783 0.503864i $$-0.168089\pi$$
0.863783 + 0.503864i $$0.168089\pi$$
$$710$$ 12.0000 0.450352
$$711$$ 0 0
$$712$$ −6.00000 −0.224860
$$713$$ 32.0000 1.19841
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −12.0000 −0.448461
$$717$$ 16.0000 0.597531
$$718$$ 32.0000 1.19423
$$719$$ −36.0000 −1.34257 −0.671287 0.741198i $$-0.734258\pi$$
−0.671287 + 0.741198i $$0.734258\pi$$
$$720$$ −1.00000 −0.0372678
$$721$$ 0 0
$$722$$ 45.0000 1.67473
$$723$$ 18.0000 0.669427
$$724$$ −2.00000 −0.0743294
$$725$$ −2.00000 −0.0742781
$$726$$ 0 0
$$727$$ −40.0000 −1.48352 −0.741759 0.670667i $$-0.766008\pi$$
−0.741759 + 0.670667i $$0.766008\pi$$
$$728$$ 0 0
$$729$$ 1.00000 0.0370370
$$730$$ 2.00000 0.0740233
$$731$$ −16.0000 −0.591781
$$732$$ −6.00000 −0.221766
$$733$$ 14.0000 0.517102 0.258551 0.965998i $$-0.416755\pi$$
0.258551 + 0.965998i $$0.416755\pi$$
$$734$$ 16.0000 0.590571
$$735$$ −7.00000 −0.258199
$$736$$ 4.00000 0.147442
$$737$$ 0 0
$$738$$ −6.00000 −0.220863
$$739$$ −24.0000 −0.882854 −0.441427 0.897297i $$-0.645528\pi$$
−0.441427 + 0.897297i $$0.645528\pi$$
$$740$$ 2.00000 0.0735215
$$741$$ −16.0000 −0.587775
$$742$$ 0 0
$$743$$ 8.00000 0.293492 0.146746 0.989174i $$-0.453120\pi$$
0.146746 + 0.989174i $$0.453120\pi$$
$$744$$ −8.00000 −0.293294
$$745$$ 10.0000 0.366372
$$746$$ −2.00000 −0.0732252
$$747$$ −4.00000 −0.146352
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 1.00000 0.0365148
$$751$$ −40.0000 −1.45962 −0.729810 0.683650i $$-0.760392\pi$$
−0.729810 + 0.683650i $$0.760392\pi$$
$$752$$ −4.00000 −0.145865
$$753$$ 20.0000 0.728841
$$754$$ 4.00000 0.145671
$$755$$ −8.00000 −0.291150
$$756$$ 0 0
$$757$$ −34.0000 −1.23575 −0.617876 0.786276i $$-0.712006\pi$$
−0.617876 + 0.786276i $$0.712006\pi$$
$$758$$ 36.0000 1.30758
$$759$$ 0 0
$$760$$ 8.00000 0.290191
$$761$$ −30.0000 −1.08750 −0.543750 0.839248i $$-0.682996\pi$$
−0.543750 + 0.839248i $$0.682996\pi$$
$$762$$ −16.0000 −0.579619
$$763$$ 0 0
$$764$$ −12.0000 −0.434145
$$765$$ −2.00000 −0.0723102
$$766$$ 12.0000 0.433578
$$767$$ −8.00000 −0.288863
$$768$$ −1.00000 −0.0360844
$$769$$ −10.0000 −0.360609 −0.180305 0.983611i $$-0.557708\pi$$
−0.180305 + 0.983611i $$0.557708\pi$$
$$770$$ 0 0
$$771$$ −26.0000 −0.936367
$$772$$ 22.0000 0.791797
$$773$$ 34.0000 1.22290 0.611448 0.791285i $$-0.290588\pi$$
0.611448 + 0.791285i $$0.290588\pi$$
$$774$$ −8.00000 −0.287554
$$775$$ 8.00000 0.287368
$$776$$ −14.0000 −0.502571
$$777$$ 0 0
$$778$$ −22.0000 −0.788738
$$779$$ 48.0000 1.71978
$$780$$ −2.00000 −0.0716115
$$781$$ 0 0
$$782$$ 8.00000 0.286079
$$783$$ 2.00000 0.0714742
$$784$$ −7.00000 −0.250000
$$785$$ 2.00000 0.0713831
$$786$$ 12.0000 0.428026
$$787$$ 32.0000 1.14068 0.570338 0.821410i $$-0.306812\pi$$
0.570338 + 0.821410i $$0.306812\pi$$
$$788$$ −10.0000 −0.356235
$$789$$ −24.0000 −0.854423
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ −12.0000 −0.426132
$$794$$ −2.00000 −0.0709773
$$795$$ 2.00000 0.0709327
$$796$$ −24.0000 −0.850657
$$797$$ −30.0000 −1.06265 −0.531327 0.847167i $$-0.678307\pi$$
−0.531327 + 0.847167i $$0.678307\pi$$
$$798$$ 0 0
$$799$$ −8.00000 −0.283020
$$800$$ 1.00000 0.0353553
$$801$$ −6.00000 −0.212000
$$802$$ 18.0000 0.635602
$$803$$ 0 0
$$804$$ 12.0000 0.423207
$$805$$ 0 0
$$806$$ −16.0000 −0.563576
$$807$$ 22.0000 0.774437
$$808$$ 6.00000 0.211079
$$809$$ −30.0000 −1.05474 −0.527372 0.849635i $$-0.676823\pi$$
−0.527372 + 0.849635i $$0.676823\pi$$
$$810$$ −1.00000 −0.0351364
$$811$$ 8.00000 0.280918 0.140459 0.990086i $$-0.455142\pi$$
0.140459 + 0.990086i $$0.455142\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ −20.0000 −0.700569
$$816$$ −2.00000 −0.0700140
$$817$$ 64.0000 2.23908
$$818$$ −26.0000 −0.909069
$$819$$ 0 0
$$820$$ 6.00000 0.209529
$$821$$ −10.0000 −0.349002 −0.174501 0.984657i $$-0.555831\pi$$
−0.174501 + 0.984657i $$0.555831\pi$$
$$822$$ −2.00000 −0.0697580
$$823$$ −24.0000 −0.836587 −0.418294 0.908312i $$-0.637372\pi$$
−0.418294 + 0.908312i $$0.637372\pi$$
$$824$$ 16.0000 0.557386
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −12.0000 −0.417281 −0.208640 0.977992i $$-0.566904\pi$$
−0.208640 + 0.977992i $$0.566904\pi$$
$$828$$ 4.00000 0.139010
$$829$$ −2.00000 −0.0694629 −0.0347314 0.999397i $$-0.511058\pi$$
−0.0347314 + 0.999397i $$0.511058\pi$$
$$830$$ 4.00000 0.138842
$$831$$ −14.0000 −0.485655
$$832$$ −2.00000 −0.0693375
$$833$$ −14.0000 −0.485071
$$834$$ 16.0000 0.554035
$$835$$ 16.0000 0.553703
$$836$$ 0 0
$$837$$ −8.00000 −0.276520
$$838$$ 4.00000 0.138178
$$839$$ −12.0000 −0.414286 −0.207143 0.978311i $$-0.566417\pi$$
−0.207143 + 0.978311i $$0.566417\pi$$
$$840$$ 0 0
$$841$$ −25.0000 −0.862069
$$842$$ 38.0000 1.30957
$$843$$ −10.0000 −0.344418
$$844$$ 0 0
$$845$$ 9.00000 0.309609
$$846$$ −4.00000 −0.137523
$$847$$ 0 0
$$848$$ 2.00000 0.0686803
$$849$$ −8.00000 −0.274559
$$850$$ 2.00000 0.0685994
$$851$$ −8.00000 −0.274236
$$852$$ 12.0000 0.411113
$$853$$ −26.0000 −0.890223 −0.445112 0.895475i $$-0.646836\pi$$
−0.445112 + 0.895475i $$0.646836\pi$$
$$854$$ 0 0
$$855$$ 8.00000 0.273594
$$856$$ −20.0000 −0.683586
$$857$$ 42.0000 1.43469 0.717346 0.696717i $$-0.245357\pi$$
0.717346 + 0.696717i $$0.245357\pi$$
$$858$$ 0 0
$$859$$ 4.00000 0.136478 0.0682391 0.997669i $$-0.478262\pi$$
0.0682391 + 0.997669i $$0.478262\pi$$
$$860$$ 8.00000 0.272798
$$861$$ 0 0
$$862$$ 24.0000 0.817443
$$863$$ 4.00000 0.136162 0.0680808 0.997680i $$-0.478312\pi$$
0.0680808 + 0.997680i $$0.478312\pi$$
$$864$$ −1.00000 −0.0340207
$$865$$ 18.0000 0.612018
$$866$$ 2.00000 0.0679628
$$867$$ 13.0000 0.441503
$$868$$ 0 0
$$869$$ 0 0
$$870$$ −2.00000 −0.0678064
$$871$$ 24.0000 0.813209
$$872$$ 6.00000 0.203186
$$873$$ −14.0000 −0.473828
$$874$$ −32.0000 −1.08242
$$875$$ 0 0
$$876$$ 2.00000 0.0675737
$$877$$ 22.0000 0.742887 0.371444 0.928456i $$-0.378863\pi$$
0.371444 + 0.928456i $$0.378863\pi$$
$$878$$ 16.0000 0.539974
$$879$$ −6.00000 −0.202375
$$880$$ 0 0
$$881$$ 58.0000 1.95407 0.977035 0.213080i $$-0.0683494\pi$$
0.977035 + 0.213080i $$0.0683494\pi$$
$$882$$ −7.00000 −0.235702
$$883$$ 4.00000 0.134611 0.0673054 0.997732i $$-0.478560\pi$$
0.0673054 + 0.997732i $$0.478560\pi$$
$$884$$ −4.00000 −0.134535
$$885$$ 4.00000 0.134459
$$886$$ −28.0000 −0.940678
$$887$$ −40.0000 −1.34307 −0.671534 0.740973i $$-0.734364\pi$$
−0.671534 + 0.740973i $$0.734364\pi$$
$$888$$ 2.00000 0.0671156
$$889$$ 0 0
$$890$$ 6.00000 0.201120
$$891$$ 0 0
$$892$$ −16.0000 −0.535720
$$893$$ 32.0000 1.07084
$$894$$ 10.0000 0.334450
$$895$$ 12.0000 0.401116
$$896$$ 0 0
$$897$$ 8.00000 0.267112
$$898$$ 10.0000 0.333704
$$899$$ −16.0000 −0.533630
$$900$$ 1.00000 0.0333333
$$901$$ 4.00000 0.133259
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 2.00000 0.0665190
$$905$$ 2.00000 0.0664822
$$906$$ −8.00000 −0.265782
$$907$$ 52.0000 1.72663 0.863316 0.504664i $$-0.168384\pi$$
0.863316 + 0.504664i $$0.168384\pi$$
$$908$$ −12.0000 −0.398234
$$909$$ 6.00000 0.199007
$$910$$ 0 0
$$911$$ −20.0000 −0.662630 −0.331315 0.943520i $$-0.607492\pi$$
−0.331315 + 0.943520i $$0.607492\pi$$
$$912$$ 8.00000 0.264906
$$913$$ 0 0
$$914$$ 38.0000 1.25693
$$915$$ 6.00000 0.198354
$$916$$ 14.0000 0.462573
$$917$$ 0 0
$$918$$ −2.00000 −0.0660098
$$919$$ −56.0000 −1.84727 −0.923635 0.383274i $$-0.874797\pi$$
−0.923635 + 0.383274i $$0.874797\pi$$
$$920$$ −4.00000 −0.131876
$$921$$ 0 0
$$922$$ −18.0000 −0.592798
$$923$$ 24.0000 0.789970
$$924$$ 0 0
$$925$$ −2.00000 −0.0657596
$$926$$ 8.00000 0.262896
$$927$$ 16.0000 0.525509
$$928$$ −2.00000 −0.0656532
$$929$$ 50.0000 1.64045 0.820223 0.572043i $$-0.193849\pi$$
0.820223 + 0.572043i $$0.193849\pi$$
$$930$$ 8.00000 0.262330
$$931$$ 56.0000 1.83533
$$932$$ 18.0000 0.589610
$$933$$ 20.0000 0.654771
$$934$$ 36.0000 1.17796
$$935$$ 0 0
$$936$$ −2.00000 −0.0653720
$$937$$ 54.0000 1.76410 0.882052 0.471153i $$-0.156162\pi$$
0.882052 + 0.471153i $$0.156162\pi$$
$$938$$ 0 0
$$939$$ 6.00000 0.195803
$$940$$ 4.00000 0.130466
$$941$$ −50.0000 −1.62995 −0.814977 0.579494i $$-0.803250\pi$$
−0.814977 + 0.579494i $$0.803250\pi$$
$$942$$ 2.00000 0.0651635
$$943$$ −24.0000 −0.781548
$$944$$ 4.00000 0.130189
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 28.0000 0.909878 0.454939 0.890523i $$-0.349661\pi$$
0.454939 + 0.890523i $$0.349661\pi$$
$$948$$ 0 0
$$949$$ 4.00000 0.129845
$$950$$ −8.00000 −0.259554
$$951$$ 6.00000 0.194563
$$952$$ 0 0
$$953$$ −38.0000 −1.23094 −0.615470 0.788160i $$-0.711034\pi$$
−0.615470 + 0.788160i $$0.711034\pi$$
$$954$$ 2.00000 0.0647524
$$955$$ 12.0000 0.388311
$$956$$ −16.0000 −0.517477
$$957$$ 0 0
$$958$$ −24.0000 −0.775405
$$959$$ 0 0
$$960$$ 1.00000 0.0322749
$$961$$ 33.0000 1.06452
$$962$$ 4.00000 0.128965
$$963$$ −20.0000 −0.644491
$$964$$ −18.0000 −0.579741
$$965$$ −22.0000 −0.708205
$$966$$ 0 0
$$967$$ 8.00000 0.257263 0.128631 0.991692i $$-0.458942\pi$$
0.128631 + 0.991692i $$0.458942\pi$$
$$968$$ 0 0
$$969$$ 16.0000 0.513994
$$970$$ 14.0000 0.449513
$$971$$ 36.0000 1.15529 0.577647 0.816286i $$-0.303971\pi$$
0.577647 + 0.816286i $$0.303971\pi$$
$$972$$ −1.00000 −0.0320750
$$973$$ 0 0
$$974$$ 8.00000 0.256337
$$975$$ 2.00000 0.0640513
$$976$$ 6.00000 0.192055
$$977$$ −38.0000 −1.21573 −0.607864 0.794041i $$-0.707973\pi$$
−0.607864 + 0.794041i $$0.707973\pi$$
$$978$$ −20.0000 −0.639529
$$979$$ 0 0
$$980$$ 7.00000 0.223607
$$981$$ 6.00000 0.191565
$$982$$ 12.0000 0.382935
$$983$$ 4.00000 0.127580 0.0637901 0.997963i $$-0.479681\pi$$
0.0637901 + 0.997963i $$0.479681\pi$$
$$984$$ 6.00000 0.191273
$$985$$ 10.0000 0.318626
$$986$$ −4.00000 −0.127386
$$987$$ 0 0
$$988$$ 16.0000 0.509028
$$989$$ −32.0000 −1.01754
$$990$$ 0 0
$$991$$ 40.0000 1.27064 0.635321 0.772248i $$-0.280868\pi$$
0.635321 + 0.772248i $$0.280868\pi$$
$$992$$ 8.00000 0.254000
$$993$$ 12.0000 0.380808
$$994$$ 0 0
$$995$$ 24.0000 0.760851
$$996$$ 4.00000 0.126745
$$997$$ −2.00000 −0.0633406 −0.0316703 0.999498i $$-0.510083\pi$$
−0.0316703 + 0.999498i $$0.510083\pi$$
$$998$$ 4.00000 0.126618
$$999$$ 2.00000 0.0632772
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 3630.2.a.n.1.1 1
11.10 odd 2 330.2.a.a.1.1 1
33.32 even 2 990.2.a.j.1.1 1
44.43 even 2 2640.2.a.n.1.1 1
55.32 even 4 1650.2.c.l.199.1 2
55.43 even 4 1650.2.c.l.199.2 2
55.54 odd 2 1650.2.a.r.1.1 1
132.131 odd 2 7920.2.a.bb.1.1 1
165.32 odd 4 4950.2.c.g.199.2 2
165.98 odd 4 4950.2.c.g.199.1 2
165.164 even 2 4950.2.a.k.1.1 1

By twisted newform
Twist Min Dim Char Parity Ord Type
330.2.a.a.1.1 1 11.10 odd 2
990.2.a.j.1.1 1 33.32 even 2
1650.2.a.r.1.1 1 55.54 odd 2
1650.2.c.l.199.1 2 55.32 even 4
1650.2.c.l.199.2 2 55.43 even 4
2640.2.a.n.1.1 1 44.43 even 2
3630.2.a.n.1.1 1 1.1 even 1 trivial
4950.2.a.k.1.1 1 165.164 even 2
4950.2.c.g.199.1 2 165.98 odd 4
4950.2.c.g.199.2 2 165.32 odd 4
7920.2.a.bb.1.1 1 132.131 odd 2